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Palak-gmat
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A string of lights is strung with red, blue, and yellow bulbs in a ratio of two to five to three, respectively. If 6 bulbs are lit in a random sequence, what is the probability that no color is lit more than twice? Can somebody please help me point out where I am going wrong.
The soln to this question can be 2 red + 2 blue + 2 yellow arrangement.
RRBBYY can be arranged in 6!/2!*2!*2! = 90 ways.
2 red lights can be chosen from 2 red lights in 1 way (2C2).
2 blue lights can be chosen from 5 yellow lights in 5C2 ways.
And 2 yellow lights can be chosen from 3 in 3C2 ways.
Total ways 6 lights can be chosen from 10 lights is 10C6 ways.
Answer = (90*2C2*5C2*3C2)/10C6
I know my answer for this probability question is wrong since it doesnt match any of the answer choices but can someone please guide me.
A) 9/10000
B) 81/1000
C) 10/81
D) 1/3
E) 80/81
Answer:B
The soln to this question can be 2 red + 2 blue + 2 yellow arrangement.
RRBBYY can be arranged in 6!/2!*2!*2! = 90 ways.
2 red lights can be chosen from 2 red lights in 1 way (2C2).
2 blue lights can be chosen from 5 yellow lights in 5C2 ways.
And 2 yellow lights can be chosen from 3 in 3C2 ways.
Total ways 6 lights can be chosen from 10 lights is 10C6 ways.
Answer = (90*2C2*5C2*3C2)/10C6
I know my answer for this probability question is wrong since it doesnt match any of the answer choices but can someone please guide me.
A) 9/10000
B) 81/1000
C) 10/81
D) 1/3
E) 80/81
Answer:B
I now understand where I was going wrong.
